Rate-independence for stresses within a granular material is a basic tenet of many models for slow dense granular flows [1,2,3,4,5]. By contrast, logarithmic rate dependence of stresses is found in solid-on-solid friction [6,7,8], in geological settings [9,10], and elsewhere [11,12,13,14]. In this work, we show that logarithmic rate-dependence occurs in granular materials for plastic (irreversible) deformations that occur during shearing but not for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate, Ω, leads to an increase in the stress and the stress fluctuations that at least qualitatively resemble what occurs due to an increase in the density. Increases in Ω also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is stopped at t = 0 , stress relaxations occur with σ(t)/σ(t = 0) ≃ A log(t/to) . This collective relaxation of the stress network over logarithmically long times provides a mechanism for rate-dependent strengthening.PACS numbers: PACS numbers: 46.10.+z, 47.20.-k Slow granular flows, the subject of this letter, are typically described in the context of Mohr-Coulomb friction models[2] that resemble those used for describing friction between two solid bodies [15]. In the well-known solid friction scenario [16,17], an object on a frictional surface will resist a force and remain at rest provided the magnitude of the tangential force is less than the product of a static friction coefficient and the normal force. This picture was translated into the granular context (for dense granular systems characterized by networks of force chains [18]) by Coulomb[19] and more recent authors [1,2], where the normal and tangential forces are replaced by corresponding normal and shear stresses, and the surface of interaction is replaced by a plane within the material. For large enough tangential force (shear stress) relative to the normal force (normal stress) sliding friction (failure in a granular material) occurs. In these pictures, sliding friction (deformation following failure) is independent of the speed of sliding (the shear rate).In reality, experiments in diverse contexts have shown that solid friction exhibits a logarithmic dependence on rate and that static frictional contacts strengthen logarithmically with age. These experiments span a vast range of lengths, and include studies at the atomic[14], lab [7,8,11,12,13], and geological scale [9,10]. Recent experiments by Ovarlez et al.[6] using granular materials sliding against the interior wall of a piston showed clear rate dependence that was associated with aging effects of individual solid-friction contacts and with the force network. Additionally, experiments by Nasuno et al. [7,8] in which a solid surface was pushed across a granular bed showed a slow strengthening (or aging) with time of the (quasi-static) force. In the present experiments, which zoom in uniquely on the grains, we show that there is a * Electronic address...